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TURBOMACHINERY (THIRD EDITION) VEDANTH KADAMBI Ex-Visiting Professor Lehigh University, Bethlehem, PA Former Professor and Head Indian Institute of Technology Kanpur, UP (INDIA) MANOHAR PRASAD Former Professor Department of Mechanical Engineering Indian Institute of Technology Kanpur, UP (INDIA) New Academic Science Limited 27 Old Gloucester Street, London, WC1N 3AX, UK www.newacademicscience.co.uk NEW ACADEMIC e-mail: [email protected] SCIENCE Copyright © 2015 by New Academic Science Limited 27 Old Gloucester Street, London, WC1N 3AX, UK www.newacademicscience.co.uk • e-mail: [email protected] ISBN : 978 1 781830 82 6 All rights reserved. No part of this book may be reproduced in any form, by photostat, microfilm, xerography, or any other means, or incorporated into any information retrieval system, electronic or mechanical, without the written permission of the copyright owner. British Library Cataloguing in Publication Data A Catalogue record for this book is available from the British Library Every effort has been made to make the book error free. However, the author and publisher have no warranty of any kind, expressed or implied, with regard to the documentation contained in this book. Preface Turbomachinery introduces the major energy conversion devices used in practice. The approach and emphasis are such as to provide enough theory along with sufficient practical detail. All the example prolems included in various chapters as well as the assigned problems have been converted to SI (System Internationale) and a set of tables of properties of steam and gases too. Specific-speed of turbines and compressors have been expressed in ‘SI unit’, in a form which is commensurate with old engineering definitions. Thermodynamics and Heat Engines are part of the study of Energy Conversion and Turbomachinery continues the same philosophy of approach assuming knowledge of both, which are basic subjects required for the understanding of Turbomachinery. The book starts with the definition of turbomachines and a comparison between positive displacement systems and turbomachines. A section on dimensional analysis, the general Euler turbine equation and its applications, the design principles of the Pelton wheel, Francis and Kaplan turbine have been treated. After traversing systematically through these, the last chapter deals with hydraulic transmissions. This book is totally dedicated to the concept and application of turbomachinery which is a principal converter of energy. The highlight of the book is its bibliography and thorough reference material given at the end of each chapter. Questions and problems to tackle for the toughest mind, have been furnished at the back of each chapter. We hope that students of mechanical engineering and teachers alike find this book a useful instrument in understanding and refreshing their knowledge in this field of Turbomachinery. We also extend our most sincere gratitude to all those who have been helpful in myriad ways toward the successful completion of this book. Contents Preface v 1. PRINCIPLES OF TURBOMACHINERY 1–40 1.1 Turbomachine 1 1.2 Positive-Displacement Devices and Turbomachines 4 1.3 Static and Stagnation States 6 1.4 First and Second Laws of Thermodynamics Applied to Turbomachines 10 1.5 Efficiency of Turbomachines 14 1.6 Performance Characteristics and Dimensional Analysis 20 References 35 Questions and Problems 36 2. ENERGY EXCHANGE IN TURBOMACHINES 41–75 2.1 Euler’s Turbine Equation 41 2.2 Fluid Energy Changes 46 2.3 Impulse and Reaction 49 2.4 Turbines, Utilization Factor 54 2.5 Compressors and Pumps 64 References 72 Questions and Problems 72 3. FLOW THROUGH NOZZLES AND BLADE PASSAGES 76–112 3.1 Introduction 76 3.2 Steady Flow through Nozzles 77 3.3 Properties of Steam and Isentropic Expansion 81 3.4 Area Changes in One-dimensional Isentropic Flow 89 3.5 Characteristics of Convergent-Divergent Nozzles 92 viii Contents 3.6 Effects of Friction in Flow Passages 93 3.7 Flow of Wet Steam through Nozzles 97 3.8 Diffusers 106 References 109 Questions and Problems 110 4. STEAM AND GAS TURBINES 113–154 4.1 The Steam Turbine 113 4.2 Impulse Staging 114 4.3 Velocity and Pressure Compounding 114 4.4 Effects of Blade and Nozzle Losses 118 4.5 Reaction Staging 128 4.6 Reheat Factor in Steam Turbines 135 4.7 Losses in Steam Turbines 138 4.8 Problem of Radial Equilibrium 141 4.9 Performance Characteristics of Steam Turbines 144 References 151 Questions and Problems 151 5. THERMAL DESIGN OF GAS TURBINES 155–202 5.1 Introduction 155 5.2 The Brayton Cycle for a Gas Turbine 159 5.3 Components and Materials of the Gas Turbine 161 5.4 Reheat Factor in Gas Turbines 172 5.5 Losses in Gas Turbines 176 5.6 Aerodynamic and Thermal Design 180 References 199 Questions and Problems 200 6. ROTARY FANS, BLOWERS AND COMPRESSORS 203–252 6.1 Introduction 203 6.2 Centrifugal Blower 204 6.3 Types of Vane Shape 204 6.4 Size and Speed of Machine 208 6.5 Vane Shape and Efficiency 209 6.6 Vane Shape and Stresses 209 6.7 Vane Shape and Characteristics 210 Contents ix 6.8 Actual Performance Characteristics 212 6.9 The Slip Coefficient 214 6.10 Fan Laws and Characteristics 217 6.11 Centrifugal Compressor 223 6.12 Performance of Centrifugal Compressors 226 6.13 Compressibility and Pre-swirl 227 6.14 The Axial-flow Compressor 233 6.15 Compressor Cascade Performance 236 6.16 Relevant Parameters 239 6.17 Axial-flow Compressor Performance 240 6.18 Preheat in Compressors 247 References 250 Questions and Problems 251 7. HYDRAULIC TURBINES 253–300 7.1 Hydraulic Power Utilization 253 7.2 Hydrograph and Water Power 256 7.3 Classification of Water Turbines 258 7.4 The Pelton Wheel 260 7.5 Velocity Triangles 262 7.6 Turbine Efficiency and Volumetric Efficiency 263 7.7 Working Proportions of Pelton Wheels 263 7.8 Francis and Deriaz Turbines 271 7.9 Design of a Francis Turbine 275 7.10 The Draft Tube 283 7.11 Propeller and Kaplan Turbines 287 7.12 Application of Aerofoil Theory to Propeller Blades 291 References 296 Questions and Problems 296 8. CENTRIFUGAL AND AXIAL-FLOW PUMPS 301–322 8.1 The Centrifugal Pump 301 8.2 Some Definitions 303 8.3 Pump Output and Efficiencies 304 8.4 Multi-stage Centrifugal Pumps 306 8.5 Axial-Flow or Propeller Pump 315 References 319 Questions and Problems 319 x Contents 9. CHARACTERISTICS OF HYDRAULIC TURBOMACHINES 323–344 9.1 Introduction 323 9.2 The Main Characteristics 323 9.3 Operating Characteristics 326 9.4 Constant Efficiency Curves 329 9.5 Cavitation in Hydraulic Machinery 330 References 343 Questions and Problems 343 10. POWER-TRANSMITTING TURBOMACHINES 345–363 10.1 Introduction 345 10.2 Theory 346 10.3 Fluid- or Hydraulic-Coupling 348 10.4 Torque-Converter 354 References 361 Questions and Problems 362 APPENDIX 364–389 Table A1 to A7 Table of Thermodynamic Properties INDEX 391–397 Mollier Diagram in SI Units 11 Principles of Turbomachinery 1.1 TURBOMACHINE While discussing the minimal number of components needed to constitute a heat engine [16], it was mentioned that mechanical energy output is obtained from an expander (work output device), whereas mechanical energy input to the system is due to a pump or a compressor which raises the pressure of the working fluid, a liquid or a gas. Both the expander and the pump (or compressor), are devices which provide work output or accept work input to affect a change in the stagnation state (Sec. 1.3) of a fluid. These devices are often encountered as parts of heat engines, though they can function independently as well. The principles of operation of both a work output device (e.g., an internal combustion engine of the reciprocating type) and a work input device (the reciprocating air-compressor [16]), have already been studied. In addition to these two types, there exist other devices which are invariably of the rotary1 type where energy transfer is brought about by dynamic action, without an impervious boundary that prevents the free flow of a fluid at any time. Such devices are called turbomachines. The turbomachine is used in several applications, the primary ones being electrical power generation, aircraft propulsion and vehicular propulsion for civilian and military use. The units used in power generation are steam, gas and hydraulic turbines, ranging in capacity from a few kilowatts to several hundred and even thousands of megawatts, depending on the application. Here, the turbomachine drives the alternator at the appropriate speed to produce power of the right frequency. In aircraft and heavy vehicular propulsion for military use, the primary driving element has been the gas turbine. The details of these types of machines will be provided in later chapters. The turbomachine has been defined differently by different authors, though these definitions are similar and nearly equivalent. According to Daily [1], the turbomachine is a device in which energy exchange is accomplished by hydrodynamic forces arising between a moving fluid and the rotating and stationary elements of the machine. According to Wislicenus [2], a turbomachine is characterized by dynamic energy exchange between one or several rotating elements and a rapidly moving fluid. 1 Rotary type machines such as gear pump and screw pump are positive displacement machines and work by moving a fluid trapped in a specified volume. 2 Turbomachinery Binder [3] states that a turbomachine is characterized by dynamic action between a fluid and one or more rotating elements. A definition to include the spirit of all the preceding statements would be: A turbomachine is a device in which energy transfer occurs between a flowing fluid and a rotating element due to dynamic action resulting in a change in pressure and momentum of the fluid. Mechanical energy transfer occurs into or out of the turbomachine, usually in steady flow. Turbomachines include all those types that produce large-scale power and those that produce a head or pressure, such as centrifugal pumps and compressors. The principal components of a turbomachine are: (i) A rotating element carrying vanes operating in a stream of fluid, (ii) A stationary element or elements which generally act as guide vanes or passages for the proper control of flow direction and the energy conversion process, (iii) an input and/or an output shaft, and (iv) a housing (Fig. 1.1). The rotating element carrying the vanes is also known by the names rotor, runner, impeller, etc., depending upon the particular application. Energy transfer occurs only due to the exchange of momentum between the flowing fluid and the rotating elements; there may not be even a specific boundary that the fluid is not permitted to cross. Details relating to these will be discussed in the following sections. Inlet Stator or housing Rotor Rotor blade Shaft Blade tip Stator blade Exit Fig. 1.1. Schematic cross-sectional view of a turbine showing the principal parts of the turbomachine. The stationary element is also known by different names—among them guide-blade or nozzle—depending on the particular machine and the kind of flow occurring in it. A stationary element is not a necessary part of every turbomachine. The common ceiling fan used in many buildings to circulate air during summer and the table fan are examples of turbomachines with no stationary element. Such machines have only two elements of the four mentioned above: an input shaft and a rotating blade element. Either an input or an output shaft or both may be necessary depending on the application. If the turbomachine is power-absorbing, the enthalpy of the fluid flowing through it increases due to mechanical energy input at the shaft. If the turbomachine is power-generating, mechanical energy output is obtained at the shaft due to a decrease in enthalpy of the flowing fluid. It is also possible to have power-transmitting turbomachines which simply transmit power from an input shaft to an output shaft, just like a clutch-plate gear drive in a car which transmits the power generated by the reciprocating engine to the shaft which drives the wheels. In principle, Principles of Turbomachinery 3 the device acts merely as an energy transmitter to change the speed and torque on the driven member as compared with the driver. There are many examples of a these types of machines. Examples of power-absorbing turbomachines are mixed-flow, axial-flow and centrifugal pumps, fans, blowers and exhausters, centrifugal and axial compressors, etc. Examples of power- generating devices are steam, gas and hydraulic turbines. The best known examples of power- transmitting turbomachines are fluid-couplings and torque-converters for power transmission used in automobiles, trucks and other industrial applications. The housing too is not a necessary part of a turbomachine. When present, it is used to restrict the fluid flow to a given space and prevent its escape in directions other than those required for energy transfer and utilization. The housing plays no role in the energy conversion process. The turbomachine that has housing is said to be enclosed and that which has no housing is said to be extended [4]. The ceiling-fan shown in Fig. 1.2 is an example of an extended turbomachine and all the rest shown in the figure are enclosed turbomachines. Fig. 1.2. Classification based on fluid flow in turbomachine. Turbomachines are also categorized by the direction of fluid flow as shown in Fig. 1.2. The flow directions are: (i) axial, (ii) radial and (iii) mixed. In the axial-flow and radial-flow turbomachines, the major flow directions are approximately axial and radial respectively, while in the mixed-flow machine, the flow usually enters the rotor axially and leaves radially or vice versa. Mixed flow may also involve flow over the surface of a cone. An example of a mixed- flow machine is a mixed-flow pump. A radial flow machine may also be classified into radial inward flow(centripetal) or radial outward flow(centrifugal) types depending on whether the flow is directed towards or away from the shaft axis.